### Average of a, b, and c is 11; average of c, d and e is 17; average of e and f is 22 and average of e and c is 17. Find out the average of a, b, c, d, e and f.

A. $15 \frac{2}{3}$ B. $18 \frac{1}{2}$ C. $16 \frac{1}{2}$ D. None of these Answer: Option A

### Solution(By Apex Team)

Average of a, b and c = 11 Total of a, b and c = 33…..(i) Similarly, average of c, d and e = 17 Sum of c + d + e = 3 × 17 = 51…..(ii) Average of e and f is 22 Sum of e + f = 2 × 22 = 44…..(iii) Average of e and c is 17 Sum of e + c = 2 × 17 = 34…..(iv) By equations (i) + (ii) + (iii) – (iv) a + b + c + c + d + e + e + f – e – c = 33 + 51 + 44 – 34 = 128 – 34 = 94 ∴ Required average $\begin{array}{l} =\large\frac{94}{6} \\ =\large\frac{47}{3} \\ =15 \frac{2}{3} \end{array}$

## Related Questions On Average

A. 20
B. 21
C. 28
D. 32

A. 18
B. 20
C. 24
D. 30

A. 10 years
B. 10.5 years
C. 11 years
D. 12 years

### If the arithmetic mean of 0, 5, 4, 3 is a, that of -1, 0, 1, 5, 4, 3 is b and that of 5, 4, 3 is c, then the relation between a, b, and c is.

A. a = b = c
B. a : b : c = 3 : 2 : 4
C. 4a = 5b = c
D. a + b + c = 12